Show that $\int_{\left(2,1,2\right)}^{\left(-1,-1,3\right)}f\,dx+g\,dy+h\,dz = \int_{\left(2,1,2\right)}^{\left(-1,-1,3\right)}2xy^{4}z^{2}dx+4y^{3}x^{2}z^{2}dy+2zy^{4}x^{2}dz$ is independent of path:

$\frac {\partial h}{\partial y}$ =
$\frac {\partial g}{\partial z}$ =
$\frac {\partial f}{\partial z}$ =
$\frac {\partial h}{\partial x}$ =
$\frac {\partial g}{\partial x}$ =
$\frac {\partial f}{\partial y}$ =

Therefore curl F =

$\int_{\left(2,1,2\right)}^{\left(-1,-1,3\right)}2xy^{4}z^{2}dx+4y^{3}x^{2}z^{2}dy+2zy^{4}x^{2}dz$ =